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Density of Fluid "A?"

The glass U-shaped tube contains 11 centimeters of "Fluid A" (in the left leg) above water.
Calculate the density of fluid A.

♦  Since the fluids are static, the hydrostatic equation applies. As a first task in applying the hydrostatic equation, one searches for physical scenario to find a place where the pressure is known. Sometimes there is no place where the pressure is known explicitly. In those cases there is usually a place where the pressure can be reasonably assumed. In this problem, the place is the the water surface on the right side; there the pressure is assumed atmospheric. We write the hydrostatic path from there downward through the bend then upward through both fluids to arrive at the surface of Fluid A (in the left leg).

patm + ρwatergo (0.08m) - ρAgo(0.13 m) = patm.

The "principle" was applied above. So go ahead and do algebra to it!

ρA = (8/13)ρwater = (8/13) 62.4 lbm/ft³

Therefore we determine the density to be:    ρA = 38.4 lbm/ft³.

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